Question

How can I calculate the number of photons emitted per second?

Answer 1

Hint: We can calculate the number of photons by the formula $E=nh\nu$, where E is the energy of the quanta, n is an integer, h is the Planck's constant, and $\nu$ is the frequency of the photons.

Complete answer:
We know that the active metal surface has free electrons on which light of suitable frequency falls; the free electron will jump from the ground state to the excited state. This method or this phenomenon is known as the Photometric effect. So, these electrons have some energy that is absorbed when it is excited or it is emitted when it returns back to the ground state. This energy was calculated by Max Plank in 1900 and gave his theory as Planck's quantum theory. This theory says that:
(i)- The energy will not be continuously absorbed or emitted but discontinuously in the form of small discrete packets of energy which is known as ‘quantum’ and in the case of light this is known as ‘photon’.
(ii)- So, the energy of the quantum is directly proportional to the frequency and it is written as:
$E\propto \nu$
$E=h\nu$
Where h is the Planck's constant.
(iii)- This total energy emitted or absorbed will always be in the whole number:
$E=nh\nu$
We know n is the number and frequency are calculated in $c{m}^{-1}$, so when we divide the energy of the photon or quantum then we get the number of photons or quantum per second. Its equation will be:
${\displaystyle \frac{E}{h}}=n\nu$

Note:
This theory was used to explain both photometric effect and Black Body radiations. For calculation the value of Planck's constant is taken are either $6.626\text{ x 1}{\text{0}}^{-27}erg\sec$ or $6.626\text{ x 1}{\text{0}}^{-34}joule\text{ sec}$.